Remember, multiplication is the shortcut for doing repeated addition:
\(6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 54\)
\(6 \times 9 = 54\)

Similarly, there is a shortcut to writing multiplication if you do the same thing over and over again:
\(2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 128\)

Here we multiplied 2 together 7 times.

For the shorthand, we write \(2^7 = 128\)

That little 7 means the number of times that we multiply 2 by itself and is called an exponent; sometimes we call it a power.

Here are a couple more examples:

\(5^3 = 5 \times 5 \times 5=125\)
\(7^2 = 7 \times 7 = 49\)
\(2^4 = 2 \times 2 \times 2 \times 2 = 16\)

Some of the easiest to calculate are the powers of 10. Try these:

\(10^2 = 100\)
\(10^4 = 10,000\)
\(10^8 = 100,000,000\)

Notice a pattern?

Scripture Connection

Alma 37:6

Like the small and simple things in this scripture, exponents also bring about great things. They are tiny numbers that make a big difference on the outcome of the answer.

Video Source (02:36 mins) | Transcript

Video Source (02:29 mins) | Transcript

Additional Resources

• Khan Academy: Introduction to Exponents (03:02 mins, Transcript)

Practice Problems

1. \(1^2\, = \,?\) (
   Solution

   x

   Solution: 1
   Details: Anytime 1 is used in multiplication, the answer is the other factor (numbers used in a multiplication problem). In this example \(1^2 = 1 \times 1 = 1\)
   )
2. \(8^2\, = \,?\) (
   Video Solution

   x

   Solution: 64
   Details:
   

   
   (Video Source | Transcript)
   )
3. \(0^3\, = \,?\) (
   Solution

   x

   Solution: 0
   Details:
   As we’ve seen in multiplication, any number multiplied by zero is 0:
   \(0^3 = 0 × 0 × 0 = 0\)
   )
4. \(5^3\, = \,?\) (
   Solution

   x

   Solution: 125
   Details:
   \(5^{3}\) means 5 is being multiplied to itself 3 times.
   
   \(5 \times 5 \times 5\)
   
   Since everything is being multiplied together, we can start on the left and move right, doing one operation at a time.
   
   
   \((5 \times 5) \times 5 =\)
   
   \(25 \times 5 =\)
   
   Our final answer is: 125
   )
5. \(4^3\, = \,?\) (
   Video Solution

   x

   Solution: 64
   Details:
   

   
   (Video Source | Transcript)
   )
6. \(3^4\, = \,?\) (
   Solution

   x

   Solution:
   81
   )

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